Many
people
know the "Twin Paradox". It shows that, if one of the twins
travels at large velocities, his age appears younger than the
other
twin, who did not travel. This application of relativity is well
known,
but of course such experiment has never been done and cannot be
verified experimentally. It is more challenging to
consider a
paradox
that has already been verified experimentally. Let us
examine the
"Earth Paradox".

------------------------------------------------------Earth Paradox

Let us use a very accurate method of measuring the size of the
Earth.
From a location on the equator, let us use the international
primary
standard of length to measure a distance of about 300 meters along
the
equator. In fact, the exact distance is really 299.792458 meters
so
that this distance is exactly one microsecond-light.
At
that
distance, we draw a line on the ground. Then we repeat the same
measurement along the Earth equator for another similar distance
of 300
meters, and we draw another line. This procedure is repeated
thousands
of times until the full circle around the Earth is completed and
the
experimenter arrives again at the point of departure. This
is
illustrated below on figure 1. We find that the number
of
lines drawn
on the Earth equator is about 133 425.
In the second part of the experiment, we send a beam of light
around
the Earth equator. We can anticipate that at each microsecond, the
beam
of light passes each line drawn on the ground, because they have
been
spaced by one microsecond-light (by definition). When we
send the
beam
eastward, light goes across 133425 lines, and therefore take
133425
microseconds to go around the world, passing each line every
microsecond. Also, when we send the beam westward, the beam
of
light
also passes one line every micro-second, so that light takes
133425 to
complete the trip around the world. Of course, the experiment is
well
done and light is traveling inside a vacuum pipe in which air has
been
completely pumped out. However,
following the Sagnac effect published in 1914 it has been shown
experimentally that light takes a longer time to go around the
world
Eastward than Westward. The Sagnac effect is well known. It has
been
added in the Global Positioning System (GPS) to determine time and
coordinates on Earth. The Sagnac effect is also used in optical
gyroscopes. It is very well extablished.

----------------------------------

How can the experiment above with light moving across each of the
133425 lines every microsecond be compatible with the observed
Sagnac
effect? How can the time taken, to go around the world be longer
when
going Eastward then Westward, since there are the same number of
lines
(133425)? Light takes exactly one microsecond to go between
lines
(by
definition).

===================

The answer to this problem will be given (and explained) here as
soon
as I have time to write it down, probably during the first part of
2000. Make a bookmark
if you
want to remember the Web address.